The use of amorphous patterns for the prevention of nesting in wound rolls of three dimensional sheet products has been disclosed in commonly-assigned, co-pending U.S. patent application Ser. No. 08/745,339 now U.S. Pat. No. 5,965,235, filed Nov. 8, 1996 in the names of McGuire, Tweddell, and Hamilton, entitled "Three-Dimensional, Nesting-Resistant Sheet Materials and Method and Apparatus for Making Same", the disclosure of which is hereby incorporated herein by reference. In this application, a method of generating amorphous patterns with remarkably uniform properties based on a constrained Voronoi tesselation of 2-space was outlined. Using this method, amorphous patterns consisting of an interlocking networks of irregular polygons are created using a computer.
The patterns created using the method described in the above mentioned application work quite well for flat, small materials. However, when one tries to use these patterns in the creation of production tooling (such as embossing rolls or belts), there is an obvious seam where the pattern "meets" as it is wrapped around the roll or belt due to the diverse edges of the pattern. Further, for very large rolls or belts, the computing time required to generate the pattern to cover these rolls or belts becomes overwhelming. What is needed then, is a method of creating these amorphous patterns that allows "tiling." As utilized herein, the terms "tile", "tiling", and "tiled" refer to a pattern or pattern element comprising a bounded region filled with a pattern design which can be joined edge-wise to other identical patterns or pattern elements having complementary but non-identical edge geometries to form a larger pattern having no visually-apparent seam. If such a "tiled" pattern were used in the creation of an embossing roll, there would be no appearance of a seam where flat the pattern "meets" as it is wrapped around the roll. Further, a very large pattern (such as the surface of a large embossing roll) could be made by "tiling" a small pattern, and there would be no appearance of a seam at the edges of the small pattern tiles.
Notwithstanding the development of various patterns, there remains the difficult task of forming an endless apertured belt of material to serve as a forming structure for forming three-dimensional webs with patterns of protrusions corresponding to apertures in the belt. Prior art belt forming techniques generally rely upon welding or fusing non-apertured ends of the belt material together and drilling holes therethrough to approximate the appearance of the patterned apertures. However, particularly with amorphous patterns, the regular nature of drilled holes creates a readily visibly discernible seam in the belt, and hence a corresponding interruption in the pattern of protrusions in the finished product. Forming patterned apertures all the way to the ends of the belt material likewise creates a difficult challenge in terms of satisfactorily fusing discontinuous end edges of the material together. For example, a commonly used method of converting a thin metal strip into a cylindrical belt is by butt-welding the strip into a cylinder using a high energy beam (electron beam or laser beam) as the energy source. One requirement of this welding step is that the welding be carried out across a continuous strip of metal. Interruptions in the metal cause the welding to be inaccurate and discontinuous as holes are left by the beam at the entrance and exit of a weld line.
Accordingly, it would be desirable to provide a method of creating continuous apertured belts with no readily discernible seam or interruption in amorphous patterns of apertures.